A lot of people don't know how to feel towards death because we've never experienced it. It's totally confusing in many ways. Sometimes it doesn't even seem real. It can be difficult to wrap your mind around the fact that a person or a dog in this case is here one day and gone the next, but never returning in any way, shape or form. To exist one moment and not the next is truly beyond our capabilities as humans to fully comprehend, no matter how OK we think we are with death.
I also think the brunt of the pain that accompanies loss is often delayed. It takes a while for the true meaning of death to hit you, but when it does you never can be quite sure what you'll feel.